In closing let us note some further applications and additional developments of our study here. Firstly, it would be interesting to study in more detail the linear case especially in regard with its cosmological implications in the presence of the cosmological hyperfluid [1]}, [2]}. In addition, as we have already mentioned, it would be worthy to elaborate more on the coupled scalar field we presented when both torsion and non-metricity are allowed and direct couplings of the latter with the scalar field occur. Finally, it would be quite interesting to go beyond linear functions \(F\)  of the new dilation current term we considered. In this way we will be able to investigate what exactly is the effect of this new addition/extension as well as its phenomenology especially with regards to its energy momentum trace counterpart.
